已知数列{an}是公比大于1的等比数列,对任意的n∈N*有,an+1=a1+a2+...+an-1+5/2an+1/21.求数列{an}的通项公式2.设数列{bn}满足:bn=1/n(log3(a1)+log3(a2)+...+log3(an)+log3(t))(n∈N*),若{bn}为等差数列,求
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![已知数列{an}是公比大于1的等比数列,对任意的n∈N*有,an+1=a1+a2+...+an-1+5/2an+1/21.求数列{an}的通项公式2.设数列{bn}满足:bn=1/n(log3(a1)+log3(a2)+...+log3(an)+log3(t))(n∈N*),若{bn}为等差数列,求](/uploads/image/z/11576920-40-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E6%98%AF%E5%85%AC%E6%AF%94%E5%A4%A7%E4%BA%8E1%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84n%E2%88%88N%2A%E6%9C%89%2Can%2B1%3Da1%2Ba2%2B...%2Ban-1%2B5%2F2an%2B1%2F21.%E6%B1%82%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F2.%E8%AE%BE%E6%95%B0%E5%88%97%EF%BD%9Bbn%EF%BD%9D%E6%BB%A1%E8%B6%B3%EF%BC%9Abn%3D1%2Fn%28log3%28a1%29%2Blog3%28a2%29%2B...%2Blog3%28an%29%2Blog3%28t%29%29%28n%E2%88%88N%2A%29%2C%E8%8B%A5%EF%BD%9Bbn%EF%BD%9D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E6%B1%82)
已知数列{an}是公比大于1的等比数列,对任意的n∈N*有,an+1=a1+a2+...+an-1+5/2an+1/21.求数列{an}的通项公式2.设数列{bn}满足:bn=1/n(log3(a1)+log3(a2)+...+log3(an)+log3(t))(n∈N*),若{bn}为等差数列,求
已知数列{an}是公比大于1的等比数列,对任意的n∈N*有,an+1=a1+a2+...+an-1+5/2an+1/2
1.求数列{an}的通项公式
2.设数列{bn}满足:bn=1/n(log3(a1)+log3(a2)+...+log3(an)+log3(t))(n∈N*),若{bn}为等差数列,求实数t的值以及数列{bn}的通项公式
已知数列{an}是公比大于1的等比数列,对任意的n∈N*有,an+1=a1+a2+...+an-1+5/2an+1/21.求数列{an}的通项公式2.设数列{bn}满足:bn=1/n(log3(a1)+log3(a2)+...+log3(an)+log3(t))(n∈N*),若{bn}为等差数列,求
an=a1.q^(n-1)
a(n+1)=a1+a2+...+a(n-1)+(5/2)an+1/2
n=1,
a2=(5/2)a1+1/2
a1q =(5/2)a1+1/2 (1)
n=2,
a3=a1+(5/2)a2+1/2
a1q^2=a1+(5/2)a1q+1/2 (2)
(2)-(1)
q(q-1) =-(3/2) +(5/2)q
2q^2-7q+3=0
(2q-1)(q-3)=0
q=3 (q>1)
from (1)
a1q =(5/2)a1+1/2
3a1=(5/2)a1+1/2
a1=1
ie
an= 3^(n-1)
(2)
bn=b1+(n-1)d
bn=(1/n)[ log(a1)+log(a2)+...+log(an)+log(t) ]
=(1/n)[ n(n-1)/2 +log(t) ]
n=1,
b1 =log(t) (3)
n=2,
b2=(1/2)[ 1 +log(t) ]
b1+d =(1/2)[ 1 +log(t) ] (4)
(4)-(3)
d= (1/2)[ 1 -log(t) ]
n=3,
b3=(1/3)[ 3 +log(t) ]
b1+2d=(1/3)[ 3 +log(t) ] (5)
(5)-(4)
d = 1/2 -(1/6)log(t)
(1/2)[ 1 -log(t) ] =1/2 -(1/6)log(t)
t=1
d=1/2
b1=0
bn= (n-1)/2